Explore the intricate relationship between the classification of finite simple groups (CFSG) and combinatorics in this 43-minute lecture by Tao Feng at BIMSA. Delve into the dual role of CFSG as a tool for studying highly symmetric combinatorial configurations and as a framework for solving permutation group theory problems through combinatorial analysis. Examine recent developments in both aspects and discover innovative approaches that incorporate algebraic tools from number theory and representation theory to construct and classify important geometric structures beyond the scope of CFSG.